Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 31 (2021), No. 2, 439--458Copyright Heldermann Verlag 2021 Classification of Finite Dimensional Nilpotent Lie Superalgebras by their Multipliers Saudamini Nayak Institute of Mathematics and Applications, Bhubaneswar, India anumama.nayak07@gmail.com [Abstract-pdf] Let $L$ be a nilpotent Lie superalgebra of dimension $(m\mid n)$ and $$s(L) = \frac{1}{2}[(m + n - 1)(m + n -2)]+ n+ 1 - \dim \mathcal{M}(L),$$ where $\mathcal{M}(L)$ denotes the Schur multiplier of $L$. Here $s(L)\geq 0$ and the structure of all non-abelian nilpotent Lie superalgebras with $s(L)=0$ is known from a previous publication of the author [{\em Multipliers of nilpotent Lie superalgebras}, Comm. Algebra 47/2 (2019) 689--705]. This paper is devoted to obtain all nilpotent Lie superalgebras $L$ when $s(L) \leq 2$. Further, we apply those results to list all non-abelian nilpotent Lie superalgebras $L$ with $t(L) \leq 4$. Keywords: Nilpotent Lie superalgebra, multiplier, special Heisenberg Lie superalgebra. MSC: 17B30; 17B05. [ Fulltext-pdf  (161  KB)] for subscribers only.